Mixed factors factorise: 3m - 15- 5n + mn=?

Question

So i have to factorise:

3m - 15- 5n + mn=

the answer is supposed to be
(m - 5) (3 + n)
but idk how to approach the question

Answer 1

good question.

Start by trying putting the m’s together:

m(3+n)

now, can that 3+n be useful with the other terms?

-15 -5n

yes it looks like -5(3+n)

so, put together you get

(m-5)(3+n)

 

Would that have worked the other way? That is, what if you collected n‘s first?

 

mn-5n

so we factor out the n

n(m-5)

can we use m-5 in the other terms?

3m-15

yes we can

3(m-5)

put together

(n+3)(m-5)